Geometric Horizons: A Frame Approach
A. A. Coley, D. D. McNutt

TL;DR
This paper introduces a null frame approach using the Cartan-Karlhede algorithm to identify geometric horizons in black hole mergers, focusing on algebraically special curvature properties and Cartan scalars for numerical relativity applications.
Contribution
It develops a null frame method with Cartan scalars to invariantly characterize geometric horizons during black hole mergers, enhancing numerical detection techniques.
Findings
Defined algebraically preferred null frame (APNF) for GH detection
Applied Cartan-Karlhede algorithm to fix null frame invariantly
Demonstrated method on axisymmetric Kastor-Traschen spacetime
Abstract
In the numerical investigation of the physical merger of two black holes, it is crucial to locate a black hole locally. This is usually done utilizing an apparent horizon. An alternative proposal is to identify a geometric horizon (GH), which is characterized by a surface in the spacetime on which the curvature tensor or its covariant derivatives are algebraically special. This necessitates the choice of a special null frame, which we shall refer to as an algebraically preferred null frame (APNF). The GH is then identified by surfaces of vanishing scalar curvature invariants but, unfortunately, these are difficult to compute. However, the algebraic nature of a GH means that the APNF plays a central role and suggests a null frame approach to characterizing the GH. Indeed, if we employ the Cartan-Karlhede algorithm to completely fix the null frame invariantly, then all of the remaining…
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Taxonomy
TopicsAstrophysical Phenomena and Observations · Pulsars and Gravitational Waves Research · Black Holes and Theoretical Physics
